Even the gentlest of the three main budget alternatives the House rejected this week contemplated deep cuts in domestic spending programs. The Republican Michel-Latta alternative, the most conservative of the three, contemplated cuts even deeper than those approved earlier this month in the Senate.

That is one of the reasons why many members, Democrats especially, were turned off by the budgets in this recession-election year.

Now House leaders, desperate for any formula that will produce a majority on the floor, are drafting another budget that cuts deeper still.

The domestic spending cuts in Michel-Latta, which may become a base line of sorts for further action in the House, in many ways already rival and even surpass the ones Congress voted in the famous Reagan budget victories last year.

Under Michel-Latta, domestic spending would have been held $92.6 billion below the levels it will otherwise attain over the next three years. About a third of that cut was in so-called entitlement or basic benefit programs in which checks are mailed out automatically each month to all who qualify.

These entitlement programs are not subject to the annual congressional appropriations process. The remaining cuts would have come in so-called discretionary programs that are subject to that process, and which include, among many other things, most federal grants to state and local governments.

Many of these cuts would have come through freezing discretionary programs at the levels appropriated for the current fiscal year. For technical reasons, in some cases this would mean even less money next year than this; in any case, no provision would be made for inflation, and "real" or after-inflation funding levels would fall.

How Michel-Latta would have reduced some discretionary programs from the levels they would reach next year if kept even with inflation:

Employment and training, $529 million, meaning a reduction of 120,000 trainees from fiscal year 1982; transportation, $631 million, to have come out of funds for Amtrak, highway projects and the Coast Guard; space and science, $480 million, to have come out of research and NASA programs; Legal Services Corp., $141 million this year and phasing down to zero funding by 1985; the Small Business Administration, $181 million; agricultural programs, $312 million, mostly from cuts in the dairy price support program.

Perhaps more important in Michel-Latta were the cuts contemplated in programs geared specifically for the poor: Medicaid, food stamps, housing assistance, Aid to Families with Dependent Children, which is what most people think of when they say welfare, and Supplemental Security Income or SSI, which is welfare for the needly elderly, disabled and blind.

The debate over the poverty programs cuts has been, for the most part, drowned out this spring by far noisier partisan wrangling over the administration's efforts--temporarily stalled--to reduce spending in programs that are not "means-tested" such as Social Security and Medicare. More than 80 percent of the beneficiaries of those two programs for the elderly are not poor; and of those those Americans who are poor, nearly two thirds do not receive any money from them.

On the floor of the House this week, the key debate focused on the $4.9 billion in Medicare cuts proposed for fiscal year 1983 under Michel-Latta. Once a group of Democrats succeeded in restoring those funds by taking them out of the military budget, the Michel-Latta budget, as amended, lost its conservative flank and was doomed.

While the Democrats were making their stand on Medicare, they chose not to offer any amendments to restore the poverty program cuts proposed by Michel-Latta. These include:

Food Stamps. The proposed cuts would total $5 billion over the next three years, and these would be in addition to the $6 billion in cuts enacted as a part of last year's budget act.

The Michel-Latta cuts are 50 percent deeper than the food stamp reductions provided for in the budget resolution adopted last week by the Republican-controlled Senate. Finance Committee Chairman Robert J. Dole (R-Kan.) characterized the Senate cuts as already "drastic" and said they should be partly restored in conference.

By 1985, the Michel-Latta food stamp reductions would be as deep as those proposed in Reagan's February budget. A Congressional Budget Office study of that budget concluded that by 1985, it would wipe out 28 percent of all food stamp benefits now provided to the elderly and disabled and 42 percent of the benefits now going to the working poor.

Low Income Housing. The budget authority for low income housing would be cut by $22 billion next year under the Michel-Latta plan. The number is so large because under the housing account, the entire cost of a 20- or 30-year housing project is budgeted in the first year.

The effect of Michel-Latta would be to close down the pipeline of new low-income housing starts next year, and to take $5 billion away from funds previously authorized for such projects--about as Reagan first proposed.

At present, some 3.4 million households are receiving housing subsidies. Under previously enacted budget authority, that figure is to climb to 4.1 million in 1985, but the Michel-Latta budget would pare it back to 3.7 million.

In addition, many families now living in subsidized housing would face rent increases of up to 50 percent. These increases would arise from a new requirement that the value of Food Stamps be counted in determining a poor person's income base.

Medicaid. The Michel-Latta plan calls for $1.6 billion in cuts over the next three years. It would shift the burden of health care to the states and the poor themselves. The $500 million in cuts in fiscal year 1983 would be on top of the $1 billion in cuts already required by last year's budget reconciliation act.

AFDC and Child Support Enforcement. The Michel-Latta plan calls for cuts of $1.1 billion through 1985, with two-thirds of the savings coming from benefit cuts and one-third from error rate sanctions.